Calculus of Variations and Geometric Measure Theory
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E. Acerbi - G. Mingione - G. A. Seregin

Regularity results for parabolic systems related to a class of non newtonian fluids

created on 22 Oct 2002
modified on 05 Feb 2004

[BibTeX]

Published Paper

Inserted: 22 oct 2002
Last Updated: 5 feb 2004

Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
Volume: 21
Number: 1
Pages: 25-60
Year: 2004

Abstract:

We consider a class of parabolic systems of the type: $$ ut - \mbox { div } a(x,t,Du) =0 $$ where the vector field $a(x,t,F)$ exhibits non standard growth conditions. These systems arise when studying certain classes of Non Newtonian fluids such as electrorheological fluids or fluids with viscosity depending on the temperature. For properly defined weak solutions to such systems, we prove various regularity properties: higher integrability, higher differentiability, partial regularity of the spatial gradient, estimates for the (parabolic) Hausdorff dimension of the singular set.

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